This week we have witnessed scenes in Woolwich that are the stuff of nightmares. The savage murder of Drummer Lee Rigby raises feelings of horror, anger and despair. The nation is in shock.

But have also witnessed inspirational scenes of courage. We should remember Cub Scout leader Ingrid Loyau-Kennett, who jumped off a bus passing the carnage to see if she could use her first-aid skills to help. When she realised that the death was not an accident but deliberate, she confronted the perpetrators and talked to them in the hope of preventing them from attacking anyone else. Equally admirable were the “Angels of Woolwich”, Amanda Donnelly and her daughter Gemini Donnelly-Martin, who stayed with Drummer Rigby while he lay dying. Mrs Donnelly’s son later said: “She only wanted to help the poor guy – she’s a mum. That’s what mums do.”

Now is the time for politicians from all parties and for civil servants to show courage when it comes to dealing with the preachers of hate. Britain is a tolerant and diverse society, and free expression is part of being a democracy. In general, people should feel free to speak their minds and stand up for their beliefs. However, speech and literature that incite violence and impinge upon the rights of others cannot be tolerated. Radical preachers must not be given a public platform to call for death to gay people, soldiers, “infidels” or any other group that their warped ideology leads them to condemn.

In today’s paper, Eric Pickles, the Secretary of State for Communities and Local Government, writes words that are very welcome. He says that laws currently exist to ensure that preachers do not incite violence or disorder, and that the police and judiciary should not hold back from using “their powers when the line has been crossed”.

We applaud the sentiment. However, we have already heard plenty of words from politicians on this subject and seen sadly insufficient follow‑through. In the wake of the Woolwich attack, Baroness Warsi, Senior Minister of State at the Foreign and Commonwealth Office and Minister for Faith and Communities, condemned all “extremists” and attacked the BBC for giving airtime to “idiots and nutters who speak for no one but themselves”. Yet this is the same Baroness Warsi who, The Sunday Telegraph revealed last month, had addressed an event staged by the controversial Federation of Student Islamic Societies on March 25. The group has hosted numerous extremist speakers, including Anwar al-Awlaki, an al-Qaeda recruiter; Azzam Tamimi, who endorses suicide bombing; and Haitham al-Haddad, who believes that music should be banned. Baroness Warsi told the meeting that extremism was “no more prevalent” at universities than in any other part of the country. This flies in the face of evidence from the anti-extremism group Student Rights that found at least 10 instances of Islamic extremism being promoted on British campuses in April alone.

Both the Labour administration and the current Coalition government have talked tough in public but then, when it comes to implementing policy, caved in to a misplaced fear about offending the cultural sensitivities of religious minorities – even though radical Islamists in no way reflect the faith or politics of ordinary Muslims. This has led public officials to stand by while vile thoughts are articulated – and thoughts can lead to terrible actions.

The work of The Sunday Telegraph’s fearless investigative reporter Andrew Gilligan has exposed some of the sorry failures of administrations past and present. In 2009, he revealed that the Labour government had given £113,411 to a foundation linked to Hizb ut-Tahrir – an extremist Islamic group that called for the destruction of the British state – to help finance a chain of schools. Hizb declared openly that its goal was to create an “Islamic personality” in the children it educated, to fight assimilation, and to teach children that “there must be one ruler of the khilafah [caliphate]”.

In 2010, when the new Government had been formed, Mr Gilligan disclosed the contents of leaked documents in which Whitehall civil servants had considered building links with radical groups, believing that such organisations might not lead to violence and could function as a “safety valve” for those tempted by terrorism. One group named was al‑Muhajiroun – despite the fact that it called 9/11 “magnificent” and has had links to one in five people convicted of terrorism in Britain for more than a decade. There is video of one of the Woolwich perpetrators, Michael Adebolajo, at an al‑Muhajiroun protest in 2007.

In spite of these policy weaknesses, the security forces have made progress in tackling extremism and there have doubtless been many successes that we shall never know about, because the violence prevented has never, thankfully, been seen. But we need to be honest about what has gone wrong. Cultural anxieties have meant that recruiting grounds for extremism have been allowed to develop in our mosques, prisons and universities.

It is time we applied the same standard to Islamist groups that promote violence that we would apply to any other lunatic fringe. The authorities need to be bold enough to call religious extremism by its proper name and, as Mr Pickles writes, police and the judiciary must act to deny a platform to those who would spread chaos and bloodshed in our society. That is exactly what ordinary, law-abiding Muslims would want our government to do. They share the outrage and disgust at the dissemination of a false gospel of violent nihilism. They, too, want to see action.

A lesson that we can all take from the Woolwich attack is to imitate the bravery of the women who faced down savagery in order to defend the innocent. If one good thing comes out of this horrific incident, let it be that we all finally have the courage to confront the preachers of hate in our midst.